Identifying critical nodes in networks is a classical decision-making task, and many methods struggle to strike a balance between adaptability and utility. Therefore, we propose an approach that empowers Evolutionary Algorithm (EA) with Large Language Models (LLMs), to generate a function called "score\_nodes" which can further be used to identify crucial nodes based on their assigned scores. Our model consists of three main components: Manual Initialization, Population Management, and LLMs-based Evolution. It evolves from initial populations with a set of designed node scoring functions created manually. LLMs leverage their strong contextual understanding and rich programming skills to perform crossover and mutation operations on the individuals, generating excellent new functions. These functions are then categorized, ranked, and eliminated to ensure the stable development of the populations while preserving diversity. Extensive experiments demonstrate the excellent performance of our method, showcasing its strong generalization ability compared to other state-of-the-art algorithms. It can consistently and orderly generate diverse and efficient node scoring functions. All source codes and models that can reproduce all results in this work are publicly available at this link: \url{https://anonymous.4open.science/r/LLM4CN-6520}

翻译：网络中的关键节点识别是一项经典的决策任务，许多方法难以在适应性与实用性之间取得平衡。因此，我们提出了一种将进化算法与大语言模型相结合的方法，生成一个名为“score_nodes”的函数，该函数可进一步用于根据节点得分识别关键节点。我们的模型由三个主要组件构成：手动初始化、种群管理和基于大语言模型的进化。它从手动创建的一组节点评分函数初始种群开始进化。大语言模型利用其强大的上下文理解能力和丰富的编程技能，对个体执行交叉和变异操作，生成优秀的新函数。这些函数随后被分类、排序和淘汰，以确保种群的稳定发展并保持多样性。大量实验表明，我们的方法具有卓越性能，与其他最先进算法相比展现出强大的泛化能力。它能稳定、有序地生成多样化且高效的节点评分函数。所有可重现本研究全部结果的源代码和模型均公开于以下链接：\url{https://anonymous.4open.science/r/LLM4CN-6520}